Tapasya means voluntary acceptance of bodily pains to achieve some higher end of life. Rāvaṇa and Hiraṇyakaśipu underwent a severe type of bodily torture to achieve the end of sense gratification. Sometimes modern politicians also undergo severe types of austerities to achieve some political end. This is not actually tapasya. One should accept voluntary bodily inconvenience for the sake of knowing Vāsudeva because that is the way of real austerities. Otherwise all forms of austerities are classified as modes of passion and ignorance. Passion and ignorance cannot end the miseries of life. Only the mode of goodness can mitigate the threefold miseries of life.
(Srimad Bhagavatam-----1:2:28-29-----purport).

There are many sages empowered with the influence of austerity and many yogīs, philosophers and renouncers who sometimes exhibit their acquired power under the influence of the Rudra principle of anger and passion. The great yogī Durvāsā, under the influence of this Rudra principle, picked a quarrel with Mahārāja Ambarīṣa, and a brāhmaṇa boy exhibited the Rudra principle by cursing the great King Parīkṣit.
(Srimad Bhagavatam-----3:12:11-----purport).

It is also said that Vasudeva and Devakī, in their previous birth as Sutapā and Pṛśni, underwent a severe type of penance to get the Lord as their son, and as a result of such austerities the Lord appeared as their son.
(Srimad Bhagavatam-----1:8:33-----purport).

The women who became the wives of the Lord are certainly not ordinary women, because to get the Lord as one's husband is the result of many, many millions of births' tapasya (austerity). When the Lord appears on different lokas, or planets, or on this planet of human beings, He displays His transcendental pastimes just to attract the conditioned souls to become His eternal servitors, friends, parents and lovers respectively in the transcendental world, where the Lord eternally reciprocates such exchanges of service.
(Srimad Bhagavatam-----1:11:35-----purport).

Devahūti engaged only in the service of Kardama Muni. She was not supposed to be so advanced in austerity, ecstasy, meditation or Kṛṣṇa consciousness, but, imperceptibly, she was sharing her husband's achievements, which she could neither see nor experience. Automatically she achieved these graces of the Lord.
(Srimad Bhagavatam-----3:23:7-----purport).

Jarāsandha was a very powerful king of Magadha, and the history of his birth and activities is also very interesting. His father, King Bṛhadratha, was also a very prosperous and powerful king of Magadha, but he had no son, although he married two daughters of the King of Kāśī. Being disappointed in not getting a son from either of the two queens, the King, along with his wives, left home to live in the forest for austerities, but in the forest he was blessed by one great ṛṣi to have a son, and he gave him one mango to be eaten by the queens. The queens did so and were very soon pregnant. The King was very happy to see the queens bearing children, but when the ripe time approached, the queens delivered one child in two parts, one from each of the queens' wombs.
(Srimad Bhagavatam-----1:15:9-----purport).

Durvāsā Muni: A powerful mystic brāhmaṇa determined to observe the principles of religion with great vows and under strict austerities. His name is associated with many historical events, and it appears that the great mystic could be both easily satisfied and easily annoyed, like Lord Śiva. When he was satisfied, he could do tremendous good to the servitor, but if he was dissatisfied he could bring about the greatest calamity. Kumārī Kuntī, at her father's house, used to minister all kinds of services to all great brāhmaṇas, and being satisfied with her good reception Durvāsā Muni blessed her with a power to call any demigod she desired.
(Srimad Bhagavatam-----1:15:11-----purport).

By designating particular places for the personality of Kali, Mahārāja Parīkṣit practically cheated Kali. In the presence of Kali, Dharma (in the shape of a bull), and the earth (in the shape of a cow), he could actually estimate the general condition of his kingdom, and therefore he at once took proper steps to reestablish the legs of the bull, namely austerity, cleanliness and mercy.
(Srimad Bhagavatam-----1:17:42-----purport).

Gādhi-suta, or Viśvāmitra: A great sage of austerity and mystic power. He is famous as Gādhi-suta because his father was Gādhi, a powerful king of the province of Kanyākubja (part of Uttara Pradesh). Although he was a kṣatriya by birth, he became a brāhmaṇa in the very same body by the power of his spiritual achievements. He picked a quarrel with Vasiṣṭha Muni when he was a kṣatriya king and performed a great sacrifice in cooperation with Maṭaṅga Muni and thus was able to vanquish the sons of Vasiṣṭha.
(Srimad Bhagavatam-----1:19:9-10-----purport).

Viśvāmitra wanted from Vasiṣṭha a cow named Nandinī, and the Muni refused to deliver it. Viśvāmitra stole the cow, and thus there was a quarrel between the sage and the King. Viśvāmitra was defeated by the spiritual strength of Vasiṣṭha, and thus the King decided to become a brāhmaṇa. Before becoming a brāhmaṇa he underwent severeausterity on the bank of the Kauśika. He was also one who tried to stop the Kurukṣetra war.
(Srimad Bhagavatam-----1:19:9-10-----purport).

Aṅgirā: He is one of the six mental sons of Brahmā and the father of Bṛhaspati, the great learned priest of the demigods in the heavenly planets. He was born of the semen of Brahmājī given to a cinder of fire. Utathya and Saṁvarta are his sons. It is said that he is still performing austerity and chanting the holy name of the Lord at a place known as Alokānanda on the banks of the Ganges.
(Srimad Bhagavatam-----1:19:9-10-----purport).

By the strength of devotional service, austerities, mystic powers and transcendental knowledge, everyone can move like Nārada Muni or Durvāsā Muni. It is said that Durvāsā Muni traveled throughout the entirety of material space and part of spiritual space within one year only. The speed of the transcendentalists can never be attained by the gross or subtle materialists.
(Srimad Bhagavatam-----2:2:23-----purport).

It was known to Śrī Nārada Muni that Lord Brahmā attained creative energy by undergoing severe austerities. As such, he could understand that there was someone else superior to Brahmājī who invested Brahmā with the power of creation.
(Srimad Bhagavatam-----2:5:4-----purport).

Sometimes great sages and ascetics enter the Himalaya Mountains in order to find seclusion from the turmoil of the world. It appears, however, that all the Pracetās, the sons of Prācīnabarhi, entered the depths of the ocean to perform austerity in a secluded place. Since they performed austerities for ten thousand years, this incident took place in the Satya-yuga, when people used to live for a hundred thousand years.
(Srimad Bhagavatam-----4:24:14-----purport).

Through austerity, King Malayadhvaja in body and mind gradually became equal to the dualities of cold and heat, happiness and distress, wind and rain, hunger and thirst, the pleasant and the unpleasant. In this way he conquered all relativities.
(Srimad Bhagavatam-----4:28:37-----purport).

Mahārāja Nābhi, although still a king. retired from family life and went with his wife to a place called Badarikāśrama in the Himalayas, where the Deity Nara-Nārāyaṇa is worshiped. The words prasanna-nipuṇena tapasā indicate that the King accepted all kinds of austerity very expertly and jubilantly. He did not at all mind leaving his comfortable life at home, although he was the emperor. Despite undergoing severe austerities and penances, he felt very pleased at Badarikāśrama, and he did everything there expertly.
(Srimad Bhagavatam-----5:4:5-----purport).

"O son of Kuntī, all that you do, all that you eat, all that you offer and give away, as well as all austerities that you may perform, should be done as an offering unto Me." (B.G.9:27) Material wealth and opulence attained through previous pious activities can be fully utilized for one's benefit in this life and the next if one is Kṛṣṇa conscious. One should not try to possess more than he needs for the bare necessities.
(Srimad Bhagavatam-----5:14:12-----purport).

The demigods, being envious of the austere life of the rigid brahmacārīs, would try to cause them to break their vows by dispatching soldiers of Cupid.
(Srimad Bhagavatam-----2:7:6-----purport).

When Lord Śiva was engaged in severely austere meditation, Cupid, the demigod of lust, threw his arrow of sex desire. Lord Śiva, thus being angry at him, glanced at Cupid in great wrath, and at once the body of Cupid was annihilated. Although Lord Śiva was so powerful, he was unable to get free from the effects of such wrath.
(Srimad Bhagavatam-----2:7:7-----purport).

Hiraṇyakaśipu underwent severe austerity and penance to satisfy Brahmā and thus receive a benediction of immortality. Actually, it is impossible even for Lord Brahmā to give anyone the benediction of becoming immortal, but indirectly Hiraṇyakaśipu received the benediction that no one within this material world would be able to kill him. In other words, because he originally came from the abode of Vaikuṇṭha, he was not to be killed by anyone within this material world. The Lord desired to appear Himself to kill him.
(Srimad Bhagavatam-----3:17:19-----purport).

Dhruva Mahārāja was the lost child of Queen Sunīti, but during his absence she always meditated upon the Supreme Personality of Godhead, who is able to rescue His devotee from all dangers. While Dhruva Mahārāja was absent from his home, not only did he undergo severe austerities in the forest of Madhuvana, but at home also his mother prayed to the Supreme Lord for his safety and good fortune. In other words, the Lord was worshiped by both the mother and the son, and both were able to achieve the supreme benediction from the Supreme Lord.
(Srimad Bhagavatam-----4:9:52-----purport).

Mahārāja Pṛthu points out that even the goddess of fortune, who is the constant companion of Lord Nārāyaṇa, specifically wanted to hear about the Lord's glories, and for the association of the gopīs, who are pure devotees, the goddess of fortune, Lakṣmī, underwent severe austerities.
(Srimad Bhagavatam-----4:20:26-----purport).

The principles of religion do not stand on some dogmas or man-made formulas, but they stand on four primary regulative observances, namely austerity, cleanliness, mercy and truthfulness.
(Srimad Bhagavatam-----1:17:25-----purport).

THFor a devotee, liberation is no problem at all. Liberation takes place without separate endeavor. Bhakti, therefore, is far better than mukti or the impersonalist position. The impersonalists undergo severe penances and austerities to attain mukti, but the bhakta, simply by engaging himself in the bhakti process, especially in chanting Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare, immediately develops control over the tongue by engaging it in chanting, and accepting the remnants of foodstuff offered to the Personality of Godhead.
(Srimad Bhagavatam-----4:25:33-----purport).

When Caitanya Mahāprabhu took sannyāsa, His wife, Viṣṇupriyādevī, although only sixteen years old, also took the vow of austerity due to her husband's leaving home. She chanted her beads, and after finishing one round, she collected one grain of rice. In this way, as many rounds as she chanted, she would receive the same number of rice grains and then cook them and so take prasāda. This is called austerity. Even today in India, widows or women whose husbands have taken sannyāsa follow the principles of austerity, even though they live with their children.
(Srimad Bhagavatam-----4:23:20-----purport).

A devotee is not concerned with enjoyment or distress; he simply desires to execute devotional service. It is said in the Śrīmad-Bhāgavatam that devotional service should be apratihatā, unchecked by the material conditions of happiness or distress. The devotee undergoes processes of austerity such as observing Ekādaśī and similar other fasting days and refraining from illicit sex life, intoxication, gambling and meat-eating. Thus he becomes purified from the reactions of his past impious life, and because he engages in devotional service, which is the most pious activity, he enjoys life without separate endeavour.
(Srimad Bhagavatam-----4:12:13-----purport).

The Supreme Lord, the Personality of Godhead, although the Lord of all followers of different paths of self-realization, is knowable only by those who are above all pretensions. Everyone is searching for eternal peace or eternal life, and with an aim to this destination everyone is either studying the Vedic scriptures or other religious scriptures or undergoing severe austerity as empiric philosophers, as mystics yogīs or as unalloyed devotees, etc. But the Supreme Lord is perfectly realized only by the devotees because they are above all pretensions.
(Srimad Bhagavatam-----2:4:19-----purport).